The correct answer is C) [tex]a_n=2\times(-4)^{n-1}[/tex].
Since it is a geometric sequence, we multiply by a constant, r, each time to find the next term.
g₂ = -8
g₅ = 512
g₂ * r * r * r = g₅
-8(r)(r)(r) = 512
-8r³ = 512
Divide both sides by -8:
-8r³/-8 = 512/-8
r³ = -64
Take the cubed root of both sides:
∛r³ = ∛-64
r = -4
Now we work backward from g₂ to find g₁:
-8/-4 = 2
We have that g₁ = 2 and r = -4. This gives us
[tex]a_n=g_1 \times r^{n-1}
\\
\\a_n=2 \times (-4)^{n-1}[/tex]
